“Twin Language” (Get Hip Records), the fourth album from the New Orleans psychedelic-rock outfit Bipolaroid, comes almost exactly 10 years to the day after the band’s first release, 2003’s “Transparent Make Believe.”

“We had our record-release party on Nov. 8, 2003, at the Circle Bar,” frontman and primary songwriter Ben Glover remembered. Kelly Keller, the bar’s proprietor, he said, was an early supporter.

“I wasn’t sure how we would fit in there, because she was really more into soul, but then we became kind of resident there,” he said. The kind of trippy, ‘60s-throwback music the band made was relatively singular at the time, though a decade down the line, he’s noticed, psychedelia has become a popular ingredient in rock n’roll. Cincinnati, New York City and Austin, Texas have all presented unrelated events called “Psych Fest” in recent years, hosting rosters of bands who interpret the word diversely, from shoegaze walls of fuzz to beachy, Brian Wilson-influenced pop.

“It’s been funny, over the years, because first it was like, ‘Why are you doing this? It’s not popular,’” Glover said. “And now it’s like, ‘Why are you doing this? It’s trendy.’

Bipolaroid has itself explored, to some extent, the wide worlds that lie underneath psychedelia’s colorful umbrella. You can hear the influence of genre classics like the Pretty Things’ “S.F. Sorrow,” or the Zombies’ “Odyssey and Oracle” on “Transparent Make Believe,” and its follow-up five years subsequent, 2008’s “E(i)ther Or.” “Illusion Fields,” released in 2010, experimented subtly with local influences, bringing in horns from the New Orleans brass-rock ensemble Egg Yolk Jubilee. Throughout, the band has been a clear acolyte of Syd Barrett, with swirling, skronky guitars and a slight, British-accented snarl to Glover’s vocals.

“Twin Language,” mixed by Nashville’s Andrija Tokic (who’s worked with the Alabama Shakes and New Orleans’ Hurray for the Riff Raff) is intentionally muddier, less complex and clean than Bipolaroid’s expansive earlier projects. The stripping down, Glover said, came about as a result of the band’s relationship with Get Hip Records, which has something of a specialty in raw, retro sounds. The label was distributing the self-released “Illusion Fields” already, and had booked Bipolaroid to play its showcase at the SXSW festival and conference in March of 2013. When Glover saw label head Gregg Kostelich in Austin, the two discussed some new songs he thought Get Hip might put out as singles.

“We had done three, and I was a little tired of albums,” said Glover. “I wanted to do 45s. I liked the process of a few songs at a time.”

Get Hip wanted a full album, though, so Glover went to the drawing board and dug up bits and pieces of songs he’d sketched out into varying levels of completion.

“And I was enjoying listening to these sketches,” he said. “I thought, why do the songs have to be seven minutes long? He likened the intention of “Twin Language” to the successfully disconnected pop clutter of “The Who Sell Out,” or the second side of “Abbey Road.”

Both of those classic albums have the feeling of a long, peculiar dream – one of those where you were, say, at the grocery store, and then suddenly your cart is gone and you find yourself at your high-school prom, but it’s not the prom, not quite. “Twin Language” has a bit of that transitional weirdness, in shifts like the punchy, jangly strummed pop that takes the 29-second “Mark Twang” into “Efflorescent Adolescent” and then the dissonant, Barrettish “Paperless Sun.”

“The direction we started going into – maybe living in New Orleans for so long started to influence me. You can hear it more so on the last album, but I need a beat nowadays.”